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arXiv · 2501.12565

The Maximum Number of Sets for 12 Cards is 14

Justin Stevens·Duncan Wilson
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Abstract

We present a novel proof that the maximum number of sets with 4 properties for 12 cards is 14 using the geometry of the finite field F_3^4, number theory, combinatorics, and graph theory. We also present several computer algorithms for finding the maximum number of sets. In particular, we show a complete set solver that iterates over all possible board configurations. We use this method to compute the maximum number of sets with 4 properties for a small number of cards, but it is generally too inefficient. However, with this method, we compute the maximum number of sets for 3 properties for all possible numbers of cards. We also present an algorithm for constructing near-optimal maximum sets.

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Justin Stevens, Duncan Wilson. 2025-01-22. The Maximum Number of Sets for 12 Cards is 14. https://arxiv.org/abs/2501.12565

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